# Wind Power Long-Term Scenario Generation Considering Spatial-Temporal Dependencies in Coupled Electricity Markets

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## Abstract

**:**

## 1. Introduction

- A new methodology to obtain realistic scenarios for wind power generation considering spatial-temporal dependencies among electricity markets is proposed. There is a lack of methodologies to generate realistic scenarios of wind power from a whole market perspective. The proposed methodology contributes to filling this gap.
- Two approaches to generate realistic wind power scenarios are proposed for the long term with a statistical approach. Most forecasting statistical approaches tackles the wind power forecasting problem from a short-term perspective. In this paper, a long-term approach with an hourly resolution is proposed.
- Finally, different strategies to evaluate the accuracy of generated scenarios are proposed and assessed at different time scales. Statistical properties of distribution functions of generated scenarios have been compared with historical data on an hourly, daily, weekly and monthly scale.

## 2. Methodology

#### 2.1. Data Pre-Processing

#### 2.2. Time Series Decomposition

#### 2.3. Detection of Spatial-Temporal Dependencies

#### 2.4. Scenario Generation

#### 2.5. Performance Evaluation

## 3. Results

^{®}, in particular, the 2018b version. For this purpose, real hourly wind power data for Spain from 2008 to 2019, and from 2012 to 2019 for Portugal and France have been analyzed. In this way, 105,192 samples for Spain and 70,128 for Portugal and France have been considered. This study case reflects the different dynamics in terms of wind resources in different regions. Data are available with the authors.

#### 3.1. Data Pre-Processing

#### 3.2. Time Series Decomposition

#### 3.3. Detection of Spatial-Temporal Dependencies

#### 3.4. Scenario Generation

#### 3.5. Performance Evaluation

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

ACF | Autocorrelation function |

AI | Artificial Intelligence |

ARIMA | Auto regressive integrated moving average model |

BIC | Bayesian information criterion |

MIBEL | Iberian electricity market |

PACF | Partial autocorrelation function |

PLF | Pinball loss function |

Quantile-quantile | |

SARIMA | Seasonal auto regressive integrated moving average model |

WS | Winkler score |

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Name | Transformation |
---|---|

Box-Cox | ${y}^{\left(\lambda \right)}=\left\{\begin{array}{cc}\frac{{y}^{\lambda}-1}{\lambda},\hfill & \mathrm{if}\phantom{\rule{4.pt}{0ex}}\lambda \ne 0\hfill \\ \mathrm{log}\left(y\right),\hfill & \mathrm{if}\phantom{\rule{4.pt}{0ex}}\lambda =0\hfill \end{array}\right.$ |

Yeo-Johnson | ${y}^{\left(\lambda \right)}=\left\{\begin{array}{cc}\frac{{(y+1)}^{\lambda}-1}{\lambda},\hfill & \mathrm{if}\phantom{\rule{4.pt}{0ex}}y\ge 0,\lambda \ne 0\hfill \\ \mathrm{log}(y+1),\hfill & \mathrm{if}\phantom{\rule{4.pt}{0ex}}y\ge 0,\lambda =0\hfill \\ -\frac{({(1-y)}^{2-\lambda}-1)}{2-\lambda},\hfill & \mathrm{if}\phantom{\rule{4.pt}{0ex}}y<0,\lambda \ne 2\hfill \\ -\mathrm{log}(1-y),\hfill & \mathrm{if}\phantom{\rule{4.pt}{0ex}}y<0,\lambda =2\hfill \end{array}\right.$ |

Logit | $z=\mathrm{ln}\left(\frac{y}{1-y}\right)$ |

Ordered quantile | $z={\mathsf{\Phi}}^{(-1)}\left(\frac{\mathrm{rank}\left(y\right)-\frac{1}{2}}{\mathrm{length}\left(y\right)}\right)$ |

Area | No Transformation | Yeo-Johnson | Logit | Box-Cox | Ordered Quantile |
---|---|---|---|---|---|

Spain | 24.77 | 8.75 | 9.67 | 3.87 | 1.14 |

Portugal | 35.28 | 15.19 | 14.92 | 5.54 | 1.11 |

France | 52.91 | 13.87 | 4.97 | 5.13 | 1.08 |

Area | Approach | P5 | P30 | P50 | P70 | P95 | Mean |
---|---|---|---|---|---|---|---|

Spain | Static | 0.0100 | 0.0444 | 0.0570 | 0.0546 | 0.0198 | 0.0372 |

Dynamic | 0.0098 | 0.0419 | 0.0519 | 0.0475 | 0.0143 | 0.0331 | |

Portugal | Static | 0.0132 | 0.0615 | 0.0793 | 0.0747 | 0.0231 | 0.0504 |

Dynamic | 0.0131 | 0.0608 | 0.0776 | 0.0724 | 0.0217 | 0.0491 | |

France | Static | 0.0087 | 0.0408 | 0.0550 | 0.0549 | 0.0188 | 0.0356 |

Dynamic | 0.0087 | 0.0402 | 0.0538 | 0.0527 | 0.0172 | 0.0345 |

Area | Approach | 50% | 80% | 90% | 98% | Mean |
---|---|---|---|---|---|---|

Spain | Static | 0.36 | 0.50 | 0.60 | 0.90 | 0.59 |

Dynamic | 0.32 | 0.43 | 0.48 | 0.58 | 0.45 | |

Portugal | Static | 0.49 | 0.64 | 0.73 | 0.89 | 0.69 |

Dynamic | 0.48 | 0.62 | 0.69 | 0.80 | 0.65 | |

France | Static | 0.35 | 0.47 | 0.55 | 0.73 | 0.52 |

Dynamic | 0.34 | 0.45 | 0.52 | 0.64 | 0.49 |

Area | Approach | P5 | P30 | P50 | P70 | P95 | Mean |
---|---|---|---|---|---|---|---|

Spain | Static | 0.0052 | 0.0230 | 0.0323 | 0.0370 | 0.0276 | 0.0250 |

Dynamic | 0.0044 | 0.0145 | 0.0160 | 0.0139 | 0.0042 | 0.0106 | |

Portugal | Static | 0.0056 | 0.0198 | 0.0250 | 0.0244 | 0.0119 | 0.0173 |

Dynamic | 0.0053 | 0.0189 | 0.0227 | 0.0196 | 0.0056 | 0.0144 | |

France | Static | 0.0043 | 0.0158 | 0.0204 | 0.0209 | 0.0118 | 0.0146 |

Dynamic | 0.0040 | 0.0140 | 0.0169 | 0.0157 | 0.0055 | 0.0112 |

Area | Approach | 50% | 80% | 90% | 98% | Mean |
---|---|---|---|---|---|---|

Spain | Static | 0.23 | 0.42 | 0.66 | 1.92 | 0.81 |

Dynamic | 0.10 | 0.15 | 0.17 | 0.26 | 0.17 | |

Portugal | Static | 0.16 | 0.26 | 0.35 | 0.72 | 0.37 |

Dynamic | 0.14 | 0.19 | 0.22 | 0.25 | 0.20 | |

France | Static | 0.14 | 0.23 | 0.32 | 0.79 | 0.37 |

Dynamic | 0.11 | 0.15 | 0.19 | 0.26 | 0.18 |

Area | Approach | P5 | P30 | P50 | P70 | P95 | Mean |
---|---|---|---|---|---|---|---|

Spain | Static | 0.0071 | 0.0300 | 0.0396 | 0.0408 | 0.0231 | 0.0281 |

Dynamic | 0.0066 | 0.0254 | 0.0300 | 0.0269 | 0.0086 | 0.0195 | |

Portugal | Static | 0.0092 | 0.0345 | 0.0423 | 0.0403 | 0.0151 | 0.0283 |

Dynamic | 0.0089 | 0.0329 | 0.0400 | 0.0372 | 0.0108 | 0.0260 | |

France | Static | 0.0060 | 0.0253 | 0.0320 | 0.0315 | 0.0138 | 0.0217 |

Dynamic | 0.0057 | 0.0241 | 0.0304 | 0.0284 | 0.0093 | 0.0196 |

Area | Approach | 50% | 80% | 90% | 98% | Mean |
---|---|---|---|---|---|---|

Spain | Static | 0.26 | 0.43 | 0.60 | 1.42 | 0.68 |

Dynamic | 0.19 | 0.26 | 0.30 | 0.39 | 0.28 | |

Portugal | Static | 0.28 | 0.40 | 0.49 | 0.77 | 0.48 |

Dynamic | 0.26 | 0.35 | 0.39 | 0.47 | 0.37 | |

France | Static | 0.21 | 0.31 | 0.40 | 0.66 | 0.39 |

Dynamic | 0.19 | 0.26 | 0.30 | 0.39 | 0.29 |

Area | Approach | P5 | P30 | P50 | P70 | P95 | Mean |
---|---|---|---|---|---|---|---|

Spain | Static | 0.0095 | 0.0413 | 0.0530 | 0.0515 | 0.0205 | 0.0352 |

Dynamic | 0.0089 | 0.0379 | 0.0471 | 0.0433 | 0.0128 | 0.0300 | |

Portugal | Static | 0.0123 | 0.0535 | 0.0681 | 0.0642 | 0.0208 | 0.0438 |

Dynamic | 0.0118 | 0.0524 | 0.0664 | 0.0617 | 0.0186 | 0.0422 | |

France | Static | 0.0082 | 0.0372 | 0.0493 | 0.0488 | 0.0172 | 0.0321 |

Dynamic | 0.0080 | 0.0364 | 0.0480 | 0.0469 | 0.0153 | 0.0309 |

Area | Approach | 50% | 80% | 90% | 98% | Mean |
---|---|---|---|---|---|---|

Spain | Static | 0.34 | 0.49 | 0.60 | 0.96 | 0.60 |

Dynamic | 0.29 | 0.38 | 0.43 | 0.52 | 0.41 | |

Portugal | Static | 0.43 | 0.58 | 0.66 | 0.82 | 0.62 |

Dynamic | 0.41 | 0.54 | 0.61 | 0.71 | 0.57 | |

France | Static | 0.31 | 0.43 | 0.51 | 0.65 | 0.48 |

Dynamic | 0.30 | 0.41 | 0.47 | 0.58 | 0.44 |

Hourly | Daily | Weekly | Monthly | |||||
---|---|---|---|---|---|---|---|---|

Areas | Hist. | Dyn. | Hist. | Dyn. | Hist. | Dyn. | Hist. | Dyn. |

Spa-Por | 0.73 | 0.68 | 0.77 | 0.71 | 0.86 | 0.81 | 0.92 | 0.91 |

Spa-Fra | 0.35 | 0.37 | 0.40 | 0.39 | 0.55 | 0.53 | 0.71 | 0.74 |

Por-Fra | 0.24 | 0.25 | 0.29 | 0.28 | 0.48 | 0.45 | 0.70 | 0.70 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Marulanda, G.; Bello, A.; Cifuentes, J.; Reneses, J. Wind Power Long-Term Scenario Generation Considering Spatial-Temporal Dependencies in Coupled Electricity Markets. *Energies* **2020**, *13*, 3427.
https://doi.org/10.3390/en13133427

**AMA Style**

Marulanda G, Bello A, Cifuentes J, Reneses J. Wind Power Long-Term Scenario Generation Considering Spatial-Temporal Dependencies in Coupled Electricity Markets. *Energies*. 2020; 13(13):3427.
https://doi.org/10.3390/en13133427

**Chicago/Turabian Style**

Marulanda, Geovanny, Antonio Bello, Jenny Cifuentes, and Javier Reneses. 2020. "Wind Power Long-Term Scenario Generation Considering Spatial-Temporal Dependencies in Coupled Electricity Markets" *Energies* 13, no. 13: 3427.
https://doi.org/10.3390/en13133427